Magnetic Flux and Faraday’s Law: Principles of Electromagnetism
Flows
To count the number of field lines crossing the loop-shaped track of your experiment, Faraday defined the concept of magnetic flux as the product of the density of the magnetic field by the vector of the loop area (perpendicular to the surface and with magnitude equal to the area). The flow through the surface or representative lines of force that traverse the surface equals the scalar product of the magnetic field and the normal to the surface considered, where the angle between the direction of the magnetic field and the normal to the surface is considered.
Faraday’s Law
In the Faraday-Henry experiment, it is observed that if the magnetic flux changes abruptly (e.g., by moving the magnet more quickly), the induced electric current intensity increases. The variation of magnetic flux with respect to time is given by Faraday’s law:
Lenz’s Law
The direction of current flowing through the coil of the Faraday-Henry experiment is defined by the so-called Lenz’s law (by the Estonian physicist Heinrich Lenz, 1804 – 1865): the current induced by a variable magnetic field takes the sense in which it tends to oppose the cause that caused it. According to Lenz’s law, bringing the magnet to the circuit generates a current that induces a magnetic field that repels the magnet (a). When the bar magnet moves away (b), the resulting current generates a field that tends to attract the magnet to the circuit.
Unification of Faraday’s and Lenz’s Laws
To unite Lenz’s and Faraday’s laws into a single principle, the term oriented spiral is defined as one in which a unique face, called the principal or positive, has been established, where the surface orients the vector. Then:
- The electromotive force (emf) induced in the loop is positive when the current generated has a clockwise sense and negative otherwise.
- The magnetic flux through a loop is oriented, where the vector represents the positive side.
Mutual Induction and Inductance
In his first experiments on the phenomenon of electromagnetic induction, Faraday did not use magnets but two coils rolled over each other with insulators. When varying the intensity of the current through one of them, an induced current is generated in the other. This is, essentially, the phenomenon of mutual induction, where the magnetic field is produced not by a magnet but by an electrical current. The variation of current in a coil results in a varying magnetic field. This magnetic field also creates a variable magnetic flux passing through the other coil and induces in it, according to the law of Faraday-Henry, an electromotive force. Any of the coils of the pair can be the inducer and any element can be induced, hence the label of mutual induction.
The phenomenon receives the name of inductance. As its name suggests, it is a self-induction current on itself. An insulated coil carrying a variable current can be thought of as also crossed by a variable flow due to its own magnetic field, which will lead to a self-induced electromotive force. In this case, the initial current is added to an additional term corresponding to the magnetic induction coil on the coil itself. All AC circuits exhibit the phenomenon of autoinduction, as they support a changing magnetic flux, but this phenomenon, albeit transient, is also present in DC circuits. In the moments when the switch is closed or opened, the current intensity varies from zero to a constant value or vice versa. This variation of intensity leads to a phenomenon of autoinduction of short duration, which is responsible for the spark that occurs in the switch when opening the circuit; the spark is the manifestation of self-induced extra current.
The Sinusoidal Electromotive Force
Faraday’s law expressed in the form of A = – A f / Ät is, strictly speaking, the average emf induced in the interval t. The induced electromotive force varies with time, taking positive and negative values in an alternative way, as does the sine function. Its maximum value depends on the intensity of the magnetic field of the magnet, the surface of the coils, the number of coils, and the speed with which the coil rotates within the magnetic field. When applied to an electrical circuit, it would lead to an alternating current.
Transformers: Lifting and Lowering Voltage
A transformer is an electric machine that can increase or decrease the voltage in an AC electrical circuit, keeping the frequency constant. These devices are based on the phenomenon of electromagnetic induction and consist, in their simplest form, of two coils wound on a closed core of iron. If an alternating emf is applied to the primary winding, variations in intensity and direction of the alternating current will create a variable magnetic field. This variable magnetic field will result in the induction of an electromotive force at the ends of the secondary winding. The relationship between the inducing emf applied to the primary winding and the induced electromotive force obtained in the secondary is directly proportional to the number of turns in the primary windings (Np) and secondary windings (Ns). Transformers are used in electrical substations of electric power transmission systems. In order to reduce Joule losses due to resistance from drivers to transport electricity over long distances, transformers are used to raise the voltage of the current generated in power plants. When it reaches its destination, it is necessary to use transformers to reduce such voltage and adapt it for use in households or industries.
Thermal Power Stations
A thermal power station is a facility used to generate electricity from heat. This heat can be obtained either from fossil fuels (oil, natural gas, or coal) or from the nuclear fission of uranium or other nuclear fuels. Power plants used in the future for nuclear fusion will also be thermoelectric. In their most classical form, power plants consist of a boiler that burns fuel to generate heat that is transferred to tubes through which water circulates, which then evaporates. The steam obtained at high pressure and temperature then expands in a steam turbine, driving an alternator whose motion generates electricity. Then the steam is cooled in a condenser by tubes that circulate cold water through an open flow from a river or a cooling tower.
Hydropower Plant
A hydropower plant is one that is used to generate electricity by harnessing the potential energy of water stored in a reservoir situated at a higher level than the plant. The water is carried by a discharge pipe to the engine room of the plant, where huge hydraulic turbines produce electricity through generators. The two main features of a hydroelectric plant, from the point of view of its electricity generation capacity, are the power of the turbine and generator and the energy.
Wind Energy
Wind energy is obtained from the wind, i.e., the kinetic energy generated by the effect of air currents or vibrations that the wind produces. Windmills have been used for centuries to grind grain, pump water, or perform other energy-intensive tasks. Currently, wind turbines are used to generate electricity, especially in areas exposed to frequent winds, such as coastal areas, high mountains, or islands. Wind energy is related to the movement of air masses moving from areas of high air pressure into adjacent areas of low pressure, with velocities proportional to the pressure gradient.